TES, you've quoted the correct version of the question, but you've taken into account the very first post lol.

We have to prove that :

Recall that
this will help you make the simplifications I'll skip

Hey ! But this is very similar to

Adding the two gives :

where and

But it can be very easily proved (or known) that

Hence

And finally, we have

But note that

Hence

Note : I've been doing all this while I'm not used at all to csc, cot, sec. What I used for simplifications is their definition in terms of cos, sin, tan. So the main difficulty for understanding is that I've been messy in my message and that I skipped some details lol